Pattern mining is an important task in AI for eliciting hypotheses from the data. When it comes to spatial data, the geo-coordinates are often considered independently as two different attributes. Consequently, rectangular shapes are searched for. Such an arbitrary form is not able to capture interesting regions in general. We thus introduce convex polygons, a good trade-off between expressiv-ity and algorithmic complexity. Our contribution is threefold: (i) We formally introduce such patterns in Formal Concept Analysis (FCA), (ii) we give all the basic bricks for mining convex polygons with exhaustive search and pattern sampling, and (iii) we design several algorithms, which we compare experimentally.